Reducing memory usage in noncoherent signal processing

ABSTRACT

A method for detecting a positioning signal includes (a) correlating a segment of a received positioning signal with a reference signal of a selected code phase and frequency to obtain a correlation value, (b) if the correlation value is less than a predetermined minimum, assigning the correlation value to the predetermined minimum, and (c) accumulating the correlation value in a sum of correlation values obtained using other segments of the received positioning signal. In addition, the correlation value may be reduced by a predetermined value, which is preferably an expected mean value for a noise component in the segment of the received positioning signal.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.10/765,651, filed Jan. 26, 2004, now U.S. Pat. No. 7,313,207, which inturn claims the benefit of U.S. Provisional Application No. 60/444,121,filed Jan. 31, 2003, the contents of which are incorporated by referencein their entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to signal detection techniques. Inparticular, the present invention relates to reducing memory usage insystems and methods that use non-coherent accumulation in detectingsignals.

2. Discussion of the Related Art

A receiver of a navigation system detects positioning signals from theGlobal Positioning System (GPS) to estimate its location. One commondetection method uses non-coherent accumulation, which is a techniquefor searching for the code phase and frequency of a received signalinvolving accumulating either the modulus, or the squared modulus, ofcomplex correlations of a reference signal and the received signal.Depending upon the relative amount of signal and noise present in thereceived signal, the correlation values will have differentdistributions. Typically, an accumulated sum is stored in memory foreach trial combination of code-phase and frequency. Signal detectionoccurs when the statistical properties of an accumulated sum indicatethat a signal is almost certainly present. Memory is a significant costin such a navigation system, as a large number of such accumulated sumsare kept in memory to achieve high resolution in detection.

A number of U.S. patent applications disclose applicable signalprocessing techniques relevant to a navigation system of the presentapplication:

-   -   1. Signal Acquisition using Data Bit Information, Ser. No.        09/888,228 filed Jun. 22, 2001, now U.S. Pat. No. 6,512,379;    -   2. Synthesizing Coherent Correlation Sums at One or Multiple        Carrier Frequencies Using Correlation Sums Calculated at a        Coarse Set of Frequencies, Ser. No. 09/888,227, filed Jun. 22,        2001, now U.S. Pat. No. 7,164,736;    -   3. Extracting Fine-Tuned Estimates from Correlation Functions        Evaluated at Limited Number of Values, Ser. No. 09/888,338,        filed Jun. 22, 2001, now U.S. Pat. No. 7,027,534;    -   4. Determining the Spatio-Temporal and Kinematic Parameters of a        Signal Receiver and its Clock by Information Fusion, Ser. No.        09/888,229, filed Jun. 22, 2001, now U.S. Pat. No. 6,542,116;    -   5. Determining Location Information Using Sampled Data        Containing Location Determining Signals And Noise Ser. No.        09/888,337, filed Jun. 22, 2001, now U.S. Pat. No. 6,535,163;    -   6. Method for optimal search scheduling in satellite        acquisition, Ser. No. 10/126,853, filed on Apr. 19, 2002, now        U.S. Pat. No. 6,836,241;    -   7. System and method to estimate the location of a receiver in a        multi path environment, Ser. No. 10/237,556, filed on Sep. 6,        2002, now U.S. Pat. No. 7,030,814;    -   8. System and method to estimate the location of a receiver,        Ser. No. 10/237,557, filed on Sep. 6, 2002, now U.S. Pat. No.        7,069,019; and    -   9. Multifunction device with positioning system and shared        processor, Ser. No. 10/286,360, filed on Nov. 1, 2002, now U.S.        Pat. No. 7,132,980.

The above copending patent applications, which are each assigned to SirFTechnology, Inc., are hereby incorporated by reference in theirentirety.

SUMMARY OF THE INVENTION

In a signal detection application, the present invention provides amethod for reducing the memory requirements for storing accumulated sumsin memory. According to one embodiment of the present invention, thedynamic range of the accumulated sum is quantized to a specified finitenumber of values. To efficiently use memory, the dynamic range isallocated to the signal portion, rather than the noise portion, of theaccumulated sum.

Thus, according to one embodiment of the present invention, a method fordetecting a positioning signal includes (a) correlating a segment of areceived positioning signal with a reference signal of a selectedcombination of code phase and frequency to obtain a correlation value,(b) if the correlation value thus obtained is less than a predeterminedminimum, assigning the correlation value to the predetermined minimum,and (c) accumulating the correlation value in a sum of correlationvalues obtained using other segments of the received positioning signal.In addition, the correlation value may be reduced by a predeterminedvalue. In one embodiment, the correlated value is reduced by an expectedmean value for a noise component in the segment of the receivedpositioning signal.

In one embodiment, the correlation value is quantized, with thepredetermined minimum value corresponding to the least quantizedcorrelation value.

In one embodiment, the sum of correlated values is compared to apredetermined threshold value corresponding to the greatest quantizedvalue. When the sum of the correlated values exceeds the predeterminedthreshold value, the accumulating of the sum of correlated values is notfurther carried out for additional segments of the received positioningsignal.

The methods of the present invention provide a memory-efficientnon-coherent accumulation.

The present invention is better understood upon consideration of thedetailed description below and the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a process of non-coherent accumulation.

FIG. 2 illustrates a process providing non-coherent accumulation withreduced memory usage, in accordance with one embodiment of the presentinvention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention provides a system and a method that improvesmemory usage efficiency of signal detection using non-coherentaccumulation over systems and methods of the prior art. In aconventional GPS application, for example, a received positioning signalof a certain duration is divided into a large number of segments, say N,and correlated with a locally generated replica of the expected GPSsignal (i.e., the code expected to be received from a GPS satellite,modulated by the expected carrier signal). If the sequence of the Ncomplex correlation values thus computed is denoted by x_(i), anon-coherent accumulation of the modulus of x_(i) can be defined as:$\sum\limits_{i = 1}^{N}{x_{i}}$

Alternatively, the accumulated value can be a sum of the squared modulusof x_(i) (i.e., $\left. {\sum\limits_{i = 1}^{N}{x_{i}}^{2}} \right),$or some other power of x_(i), to optimize memory usage, detectionsensitivity or other performance parameters.

Let σ² denote the noise power in each of the real and imaginary parts ofx_(i) (i.e., the total noise power is 2σ²), and let M denote theprobability distribution of |x_(i)|, which are assumed identicallydistributed. If the received signal contains only Gaussian white noise,then the probability density function off(M) follows a Rayleighdistribution:${f(M)} = {\frac{M}{\sigma^{2}}{\mathbb{e}}^{\frac{M^{2}}{2\sigma^{2}}}}$with a mean of M given by $\mu = {\sqrt{\frac{\pi}{2}}\sigma}$and a standard deviation of M given by$\sigma_{M} = {\sqrt{2 - \frac{\pi}{2}}{\sigma.}}$

However, if the received signal contains a GPS signal, then let S denotethe carrier to noise ratio $\frac{C}{N_{0}}$for the received signal, and the probability density function ƒ^(SIG)(M)follows a Ricean distribution:${f^{{SIG}\quad\sigma^{2}}(M)} = {\frac{M}{\sigma^{2}}{\mathbb{e}}^{\frac{M^{2} + a^{2}}{2\sigma^{2}}}{I_{0}\left( \frac{aM}{\sigma^{2}} \right)}}$with a mean of M given by$\mu_{M} = {\frac{\pi}{2}{\sigma\left( {{\left( {1 + r} \right){I_{0}\left( \frac{r}{2} \right)}} + {{rI}_{1}\left( \frac{r}{2} \right)}} \right)}{\mathbb{e}}^{- \frac{r}{2}}}$where ${r = {T\left( 10^{\frac{S}{10}} \right)}},$T being the coherent block size in seconds, and I₀ being the zero-thorder modified Bessel function of the first kind.

FIG. 1 outlines generally the steps in a process providing non-coherentaccumulation. As shown in FIG. 1, at step 101, the modulus of acorrelation value over a segment of the received signal is calculated.At step 102, which is an optional step, the modulus of the correlationvalue is quantized. At step 103, the modulus is added to a sumaccumulating the modulus of correlation values of all the segments ofreceived signal. The quantization performed at step 102 allows theaccumulating sum to be represented by a lower precision than theprecision of the computation in step 101. In determining the appropriatequantization, the memory costs is balanced against the precision lossdue to quantization. In one embodiment, a quantization of σ/2 isapplied. In the σ/2 quantization, the modulus of the correlation valueis divided by σ/2 and the result is then rounded to the nearest integer.Alternatively, instead of rounding, a floor or ceiling function can beapplied.

Non-coherent accumulation achieves two functions. First, signaldetection is achieved by comparing the accumulated sum to the expectedprobability distribution of a received signal that contains only noise.When the accumulated sum differs from that expected probabilitydistribution in a statistically significant way, a signal is deemeddetected. Second, upon detection, the frequency and code phase estimatescan be further refined by interpolating accumulation values near thepeak accumulation. In other words, the code phases and frequencies nearthe peak accumulation can be used to further improve the estimates ofcode phase and frequency.

FIG. 2 illustrates in further detail a process providing non-coherentaccumulation with reduced memory usage, in accordance with oneembodiment of the present invention. As shown in FIG. 2, at step 201,the modulus of a correlation value over a segment of the received signalis computed. At step 202, the modulus calculated at step 201 is reducedby a predetermined value. In one embodiment, the modulus is reduced bythe expected value of the noise-only modulus (i.e.,$\left. {\sigma_{M} = {\sqrt{2 - \frac{\pi}{2}}{\sigma.}}} \right)$At step 203, the reduced modulus is quantized. (Although reduction ofthe modulus by σ_(M) is described above as being carried out at step 202before quantization step 203 at a higher precision, reduction of themodulus can also occur after quantization, using a quantized value ofσ_(M).)

At step 204, the quantized reduced modulus is accumulated in anaccumulated sum. If the accumulated sum is less than a specified minimumvalue L, the accumulation sum is set to L (the “saturation” step). Thesaturation step sacrifices the ability to distinguish among lowaccumulations. However, for an appropriately chosen minimum value L, asthe low accumulations are highly unlikely to contain a detectablepositioning signal, the impact of the saturation step on signaldetection is negligible. In one embodiment, where non-coherentaccumulations are stored using 8 bits and the quantization is achievedby dividing by σ/2, the minimum value L is set to −8. L may be set to avalue even less than −8 to further reduce the impact due to thesaturating step on the distribution of the accumulated sum. L may alsobe set to a value higher than −8 to provide a larger useful dynamicrange.

In step 205, the accumulation sum is compared against a high thresholdvalue H. If the accumulated sum exceeds the high threshold value H,accumulations for the satellite of the current search are halted, sothat all accumulations will have processed the same amount of receivedsignal. By halting accumulations, the accumulations near the peak arenot saturated, and methods such as those described in the '338application can be applied to further refine estimates of code phase andfrequency. In the embodiment described above (i.e., 8-bit accumulations,σ/2 quantization, and minimum value L=−8), a high threshold value H isset to the maximum quantized value, given by 255−8=247. Alternatively,high threshold value H may be a value less than the maximum value toavoid flattening the shape of the ambiguity peak when the last term inthe accumulated sums is added. If the high threshold value H is not met,then the signal is detected by comparing the accumulated sums to a lowerthreshold determined according to the applications incorporated above.

According to the embodiment of the present invention described above,memory usage in the non-coherent accumulation is greatly reduced, whilestill allowing signal detection and estimation refinement.

The above detailed description is provided to illustrate the variousembodiments of the present invention and is not intended to be limiting.Numerous modifications and variations within the scope of the presentinvention are possible. The present invention is set forth in the claimsbelow.

1. A method for detecting a positioning signal, comprising: correlatinga segment of a received positioning signal with a reference signal of aselected code phase and frequency to obtain a correlation value; if thecorrelation value is less than a predetermined minimum, assigning thecorrelation value to the predetermined minimum; and accumulating thecorrelation value in a sum of correlation values obtained using othersegments of the received positioning signal.
 2. A method as in claim 1,further comprising reducing the correlation value by a predeterminedvalue.
 3. A method as in claim 2, wherein the correlation value isreduced by an expected mean value for a noise component in the segmentof the received positioning signal.
 4. A method as in claim 1, furthercomprising quantizing the correlation value.
 5. A method as in claim 4,wherein the predetermined minimum value is the least quantizedcorrelation value.
 6. A method as in claim 1, further comprisingcomparing the sum of correlated values to a predetermined thresholdvalue.
 7. A method as in claim 6, wherein the accumulating is notfurther carried out for additional segments of the received positioningsignal when the sum of correlated values exceeds the predeterminedvalue.
 8. A method as in claim 6, further comprising quantizing thecorrelation value, and wherein the predetermined threshold value is thegreatest quantized value.